Eye radius of category 5 cyclones is 20Km. What is the probability that any randomly selected category 5 cyclone will cross the Qld coast such that the eye wall of the cyclone will pass over Cairns which is on a 3200Km section of Qld coast?

Question

Eye radius of category 5 cyclones is 20Km. What is the probability that any randomly selected category 5 cyclone will cross the Qld coast such that the eye wall of the cyclone will pass over Cairns which is on a 3200Km section of Qld coast?
Cyclones generated in Australian waters is 10. Cyclones that crossed QLD coast 3.

Thanks for your help

drwls · Answer

30% cross the "Old" coast. 20/3200 or 1/160 is the probability the eye crosses a particular point on the coast. The overal probability is 0.3 *(1/160) = 1/533